The Tynecastle manager was on the receiving end of abuse from travelling supporters as their wait for a victory at McDiarmid Park was extended to nine years. Hearts have now won just one of 11 league matches this season.
St Johnstone, having occupied the basement spots for months, have now risen to eighth place thanks to back-to-back wins, with Hearts skipper Christophe Berra marring a solid display by deflecting a Drey Wright corner into his own net near the hour mark.
A toothless Hearts side got exactly what they deserved from a match in which they barely laid a glove on a Saints defence enjoying the novelty of a clean sheet for the first time this term.
“I understand the frustration of the supporters. Nobody wants to win games more than I do,” said Levein. “Nobody has more of a vested interest in winning than I do.
“I have no qualms in them voicing their frustration. My job is not to get overly concerned about that. My job is to win football matches.
“What doesn’t help is if the players go into their shells. You need your big players to stand up and be counted and get back into the game or score a winner. But what irritated me was it took ages to get onto the front foot and we only created a couple of late chances.
“Yesterday the league table did not look great and it’s not going to look great for the next few weeks even if we win matches. I’m not going to focus on that. I want us to try and win football matches and make the fans happy by firing on all cylinders.
Levein believes his players will lick their wounds and be prepared to face Rangers in the League Cup on Sunday.
“It’s a semi-final. I’d be surprise if anyone needed lifted. We have been very Jekyll and Hyde this season and I can’t put my finger on it.”
Saints manager Tommy Wright praised his young central defenders Jason Kerr and Wallace Duffy for nullifying the physical threat posed by Hearts centre Uchu Ikpeazu.
“The clean sheet was very important, especially since we have not been keeping them.
“We have a young defence and they will make mistakes. But I felt we defended well as a team tonight –our two centre backs did really well to nullify Hearts. They were magnificent.
“We talked before the game with the boys about possibly getting up to eighth. It’s a great win, and that’s two on the bounce now, but we will keep our feet on the ground.
“We’ve now got a free weekend coming up and then we will prepare for facing Hibs.”